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PSLE

PSLE Foundation Mathematics

<p>A company charges $\$ y$ for&nbsp;$x$ units of electricity used.<br>The charge $\$ y$ can be represented by the function $y = ux + 20$, where&nbsp;$u$ is a constant. Some corresponding values of $x$ and $y$ are given in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 600px;"><colgroup><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">$x$</th><th style="text-align: center; --cell-justify: center">$0$</th><th style="text-align: center; --cell-justify: center">$100$</th><th style="text-align: center; --cell-justify: center">$200$</th><th style="text-align: center; --cell-justify: center">$300$</th><th style="text-align: center; --cell-justify: center">$400$</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">$y$</td><td style="text-align: center; --cell-justify: center">$20$</td><td style="text-align: center; --cell-justify: center">$50$</td><td style="text-align: center; --cell-justify: center">$80$</td><td style="text-align: center; --cell-justify: center">$110$</td><td style="text-align: center; --cell-justify: center">$140$</td></tr></tbody></table></div></div>
<ol class="abc-list"><li data-list-item-id="item-a"><div class="list-item-paragraph">On the grid, draw the graph of $y = ux + 20$ for&nbsp;$0 \le x \le 400$.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-b"><div class="list-item-paragraph">Find the total cost if a household uses $140$ units of electricity.<span class="inline-marks">[1]</span></div></li><li data-list-item-id="item-c"><div class="list-item-paragraph">What does the constant term, $20$, represent?<span class="inline-marks">[1]</span></div></li><li data-list-item-id="item-d"><div class="list-item-paragraph">Find the value of $u$.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-e"><div class="list-item-paragraph">What does the gradient of the graph represent in this context?<span class="inline-marks">[1]</span></div></li></ol>

A company charges $\$ y$ for $x$ units of electricity used.
The charge $\$ y$ can be represented by the function $y = ux + 20$, where $u$ is a constant. Some corresponding values of $x$ and $y$ are given in the table below.

Gradient of a Straight Line

Plotting of Straight Line on Graph Paper

Linear Graphs in Real Life Problems

2023 ACSBR EM S1 EOY Q14

Linear Graphs and Its Applications

<p>Given that the first $5$ terms of a sequence, $T_n$, are $-2, 2, 6, 10, 14, \dots$, where&nbsp;$n = 1, 2, 3, 4$ and $5$.</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">Find a formula for the $n^{th}$ term of the sequence, $T_n$, in terms of $n$.<br>Hence find $T_0$. (Hint: substitute $n = 0$ into the formula of the general term of $T_n$.)</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">In the grid below, plot $T_n$ against $n$, i.e., draw the points of which the coordinates are in the form of $(n, T_n)$, where&nbsp;$n = 1, 2, 3, 4$ and $5$. Hence, draw a straight line that passes through these points.</div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph"><strong>Using your graph</strong>, find the gradient, $m$, and the $T_n$-intercept, $c$, of the straight line. Hence write down the equation of the straight line in the form of $T_n = mn + c$.</div></li><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">Based on your answers above, determine whether</div><ol class="abc-list"><li data-list-item-id="item-iva" data-list-item-path="item-iv/item-iva"><div class="list-item-paragraph">whether the point $\left( \frac{1}{2},-4 \right)$ lies on the graph of the straight line or not, and</div></li><li data-list-item-id="item-ivb" data-list-item-path="item-iv/item-ivb"><div class="list-item-paragraph">$-4$ is a term of the sequence $T_n$ or not. Explain your answers.</div></li></ol><div class="list-item-after-content" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767611033034-otwyfyeja5.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MTEwMzMwMzQtb3R3eWZ5ZWphNS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5Nzk2LCJleHAiOjE3OTI3MTAwOTZ9.Ym-hdDGJAUqI2i_XEg9XTLODHWc7DIv24ZRzsYfx-iM" alt="After sub-items image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div></li></ol>

Given that the first $5$ terms of a sequence, $T_n$, are $-2, 2, 6, 10, 14, \dots$, where $n = 1, 2, 3, 4$ and $5$.

**Using your graph**, find the gradient, $m$, and the $T_n$-intercept, $c$, of the straight line. Hence write down the equation of the straight line in the form of $T_n = mn + c$.

Based on your answers above, determine whether

General Term of a Sequence

Equation of a Straight Line

Testing Sequence Membership

 Number Patterns

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">On the grid below, draw the graphs of</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$y = -\frac{1}{2}x + 1$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$y = -\frac{1}{2}x - 2$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$y = -1$</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Write down the gradients of the straight lines in (i).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Based on your drawings in (i), identify the geometrical shape enclosed by the three graphs and $x$-axis.</span></div></li><li><div class="list-item-paragraph">Based on your answers in (ii) and (iii), write down ONE condition which guarantees that the two straight lines are parallel.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767605239734-ll2ofh2yesq.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDUyMzk3MzQtbGwyb2ZoMnllc3EucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTc5NiwiZXhwIjoxNzkyNzEwMDk2fQ.FihF7ohFOJ7Hwt5TVVEBdb9ERS9pK_bbldgW8t4HS2M" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li></ol>

Write down the gradients of the straight lines in (i).

Based on your drawings in (i), identify the geometrical shape enclosed by the three graphs and $x$-axis.

Based on your answers in (ii) and (iii), write down ONE condition which guarantees that the two straight lines are parallel.

Parallel and Perpendicular Lines

<ol class="i-list"><li><div class="list-item-paragraph">On the grid below, draw the graph of</div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$y = 4x - 3$,</span></div></li><li><div class="list-item-paragraph">$y = 4x + 8$</div><div class="list-item-paragraph">for value of $x$ from $-5$ to $5$.</div></li><li><div class="list-item-paragraph">$x=-1$</div></li><li><div class="list-item-paragraph">$x=1$</div><div class="list-item-paragraph">for value of $y$ from $-15$ to $15$.</div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Write down the gradients of the straight lines in (i).</span></div></li><li><div class="list-item-paragraph">Based on your drawings in (i), identify the geometrical shape enclosed by the four graphs.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767605045656-7jm00ulu9o.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDUwNDU2NTYtN2ptMDB1bHU5by5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5Nzk2LCJleHAiOjE3OTI3MTAwOTZ9.gboj0t-vuObJIUCLKfJSP2a3tN5L2Zfs2Uuuk8xUz7s" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li></ol>

Based on your drawings in (i), identify the geometrical shape enclosed by the four graphs.

Coordinate Geometry

<p>The figure below shows $\Delta ABC$ in the Cartesian plane.</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">On the same grid, mark and label the coordinates of $A$, $B$ and $C$.</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">Find the gradients of the straight lines $AB$, $BC$ and $AC$.</div></li><li data-list-item-id="item-1789466210432-35rhhnif6" data-list-item-path="item-1789466210432-35rhhnif6"><div class="list-item-paragraph"><p>In the same grid, draw the graph of $x = \frac{2}{5}$, for values of $y$ from $-1$ to $2$.</p></div><div class="graph-block" 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The figure below shows $\Delta ABC$ in the Cartesian plane.

On the same grid, mark and label the coordinates of $A$, $B$ and $C$.

Find the gradients of the straight lines $AB$, $BC$ and $AC$.

Basics of Coordinate Geometry

Gradient of Straight Line

<p>A straight line passes through $A \ (0, \frac{8}{5})$ and $B\ (2, 0)$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">In the figure below, mark and label the points $A$ and $B$. Hence draw the line $AB$.</span></div></li><li><div class="list-item-paragraph">Find the gradient and $y$-intercept of the straight line $AB$.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767604178154-rk8kixbia6.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDQxNzgxNTQtcms4a2l4YmlhNi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5Nzk2LCJleHAiOjE3OTI3MTAwOTZ9.TGUr-nuMT40ouQJl7uwYD2_XaQx7EPEpYgafgNeQq3A" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li></ol>

A straight line passes through $A \ (0, \frac{8}{5})$ and $B\ (2, 0)$.

In the figure below, mark and label the points $A$ and $B$. Hence draw the line $AB$.

Find the gradient and $y$-intercept of the straight line $AB$.

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">In the grid below, draw the graph of $y = 4 - 3x$, for values of $x$ from $-3$ to $3$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">The points $A (a, -\frac{7}{2})$, $B (b, -2)$ and $C (1, c)$ lie on the graph in (i). Using the graph you drew, find the values of $a$, $b$ and $c$.</span></div></li><li><div class="list-item-paragraph">Hence draw the points $A$, $B$ and $C$ on the graph and label their coordinates.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767603527688-251v6hhigz1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDM1Mjc2ODgtMjUxdjZoaGlnejEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTc5NiwiZXhwIjoxNzkyNzEwMDk2fQ.gSmYrfbzl5HcWZANLJ0r9pTfOdKi8mFowvWoIh8NrXo" alt="List item image" class="aligncenter custom-width" style="max-width: min(200px, 100%); height: auto;" /></div></li></ol>

In the grid below, draw the graph of $y = 4 - 3x$, for values of $x$ from $-3$ to $3$.

The points $A (a, -\frac{7}{2})$, $B (b, -2)$ and $C (1, c)$ lie on the graph in (i). Using the graph you drew, find the values of $a$, $b$ and $c$.

Hence draw the points $A$, $B$ and $C$ on the graph and label their coordinates.

Graphs of Linear Functions

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">In the grid below, draw the graph of</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$y = \frac{3}{2}x + 3$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$y = 3x - 3$</span></div></li></ol><div class="list-item-after-content">for values of $x$ from $-5$ to $5$.</div></li><li><div class="list-item-content"><span class="list-item-text">The graph of $y = \frac{3}{2}x + 3$ crosses the $x$-axis at point $A$; the graph of $y = 3x - 3$ crosses the $x$-axis at point $B$. Find the coordinates of $A$ and $B$. Hence mark and label the points $A$ and $B$ on the same grid.</span></div></li><li><div class="list-item-paragraph">Find the length of line segment $AB$.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767603361271-e0slcrcrb86.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDMzNjEyNzEtZTBzbGNyY3JiODYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTc5NiwiZXhwIjoxNzkyNzEwMDk2fQ.vCoIXVlRsHkmzH2K-W9Bv5KPfRpCf_CI9ZczEtp1V1U" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li></ol>

The graph of $y = \frac{3}{2}x + 3$ crosses the $x$-axis at point $A$; the graph of $y = 3x - 3$ crosses the $x$-axis at point $B$. Find the coordinates of $A$ and $B$. Hence mark and label the points $A$ and $B$ on the same grid.

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">In the grid below, draw the graph of</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$y = 2x + 5$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$y = -4x$</span></div></li></ol><div class="list-item-after-content">for values of $x$ from $-5$ to $5$.</div></li><li><div class="list-item-content"><span class="list-item-text">The graph of $y = 2x + 5$ crosses the $x$-axis at point $A$ and $y$-axis at point $B$. Find the coordinates of $A$ and $B$. Hence mark and label the points $A$ and $B$ on the same grids.</span></div></li><li><div class="list-item-paragraph">Find the area of $\Delta ABO$ in unit$^2$.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767603114883-yfkyowv14u9.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDMxMTQ4ODMteWZreW93djE0dTkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTc5NiwiZXhwIjoxNzkyNzEwMDk2fQ.PDlWgz4IdICUvd-ZA1St8tqHgO6DKEM24_niDyUHzYY" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li></ol>

The graph of $y = 2x + 5$ crosses the $x$-axis at point $A$ and $y$-axis at point $B$. Find the coordinates of $A$ and $B$. Hence mark and label the points $A$ and $B$ on the same grids.

Find the area of $\Delta ABO$ in unit$^2$.

Area of Rectilinear Figures

<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">The equation of a function is $y = \frac{1}{3}x + 2$. Complete the following table.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767602893160-3531xoxvpk.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDI4OTMxNjAtMzUzMXhveHZway5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5Nzk2LCJleHAiOjE3OTI3MTAwOTZ9.Ga78mhmfz7tlzeTqLrtXbhODZjg12WRrgWgclCgF6fw" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">In the grid below, draw the graph of $y = \frac{1}{3}x + 2$.</div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">Using your graph, find the value of $x$ when&nbsp;$y = \frac{2}{3}$. Hence mark and label the point in the same grid.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767602911631-tcn5vtychj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDI5MTE2MzEtdGNuNXZ0eWNoai5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5Nzk2LCJleHAiOjE3OTI3MTAwOTZ9.lIZKruGwemRrvkaAqBnRd-FZgjaM_qiu4DxnZ2WdZOA" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li></ol>

In the grid below, draw the graph of $y = \frac{1}{3}x + 2$.

<ol class="i-list"><li><div class="list-item-paragraph">The equation of a function is $y = -\frac{1}{3}x + 2$. Complete the following table.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767602510734-tgck3z28u7h.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDI1MTA3MzQtdGdjazN6Mjh1N2gucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTc5NiwiZXhwIjoxNzkyNzEwMDk2fQ.NQdBfrqcBdtVOx2u0ga1patTwJ5oaVMctvBVCSkcE2c" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div></li><li><div class="list-item-content"><span class="list-item-text">In the grid below, draw the graph of $y = -\frac{1}{3}x + 2$.</span></div></li><li><div class="list-item-paragraph">Using your graph, find the value of $y$ when $x = -1$. Hence mark and label the point in the same grid.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767602545828-67bvgt7ev3q.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDI1NDU4MjgtNjdidmd0N2V2M3EucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTc5NiwiZXhwIjoxNzkyNzEwMDk2fQ.A26iwGM7IF_lI-5pq2Ykw1VR_qtQi0cIxAAbUqcTEB4" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li></ol>

The equation of a function is $y = -\frac{1}{3}x + 2$. Complete the following table.

In the grid below, draw the graph of $y = -\frac{1}{3}x + 2$.

Using your graph, find the value of $y$ when $x = -1$. Hence mark and label the point in the same grid.

<ol class="abc-list"><li><div class="list-item-paragraph">Given that&nbsp;$y=1-3x$, copy and complete the following table.</div><div class="table-container"><table style="table-layout: fixed; width: 490px;"><colgroup><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">$x$</th><th style="text-align: center; --cell-justify: center">$-3$</th><th style="text-align: center; --cell-justify: center">$-2$</th><th style="text-align: center; --cell-justify: center">$-1$</th><th style="text-align: center; --cell-justify: center">$1$</th><th style="text-align: center; --cell-justify: center">$2$</th><th style="text-align: center; --cell-justify: center">$3$</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">$y$</td><td style="text-align: center; --cell-justify: center">$10$</td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: center; --cell-justify: center">$-2$</td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div></li><li><div class="list-item-paragraph">Using a scale of $2$ cm to represent $1$ unit on the $x$-axis and $2$ cm to represent $2$ units on the $y$-axis, draw the graph of $y=1-3x$ for values of $x$ from $-3$ to $3$.</div></li><li><div class="list-item-paragraph">Using your graph, find the value of </div><ol class="i-list"><li><div class="list-item-paragraph">$y$ when&nbsp;$x=1.5$,</div></li><li><div class="list-item-paragraph">$x$ when&nbsp;$y=1$.</div></li></ol></li><li><div class="list-item-paragraph">Hence, or otherwise, find the gradient of the graph.</div></li></ol>

Graphing and Interpreting a Linear Function

<ol class="abc-list"><li><div class="list-item-paragraph">Complete this table of values for $y=5x-2$.</div><div class="table-container"><table><thead><tr><th style="text-align: left; --cell-justify: flex-start">$x$ </th><th style="text-align: left; --cell-justify: flex-start">$-2$ </th><th style="text-align: left; --cell-justify: flex-start">$0$</th><th style="text-align: left; --cell-justify: flex-start">$6$ </th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">$y$ </td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div></li><li><div class="list-item-paragraph">On the sheet of graph paper, using a scale of $2$cm to represent $1$ unit on the $x$-axis and $2$cm to represent $5$ units on the $y$-axis, draw the graph of the linear function $y=5x-2$ for $-2\le x\le 6$.</div></li><li><div class="list-item-paragraph">From the graph, find the</div><ol class="i-list"><li><div class="list-item-paragraph">value of $y$ when $x=3$ ,</div></li><li><div class="list-item-paragraph">the gradient of the equation $y=5x-2$.</div></li></ol></li></ol>

Table of Values and Graph of a Linear Function

<ol class="abc-list"><li><div class="list-item-paragraph">Complete this table of values for&nbsp;$y=-2x+3$.</div><div class="table-container"><table style="table-layout: fixed; width: 400px;"><colgroup><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">$x$ </th><th style="text-align: center; --cell-justify: center">$-2$</th><th style="text-align: center; --cell-justify: center">$0$</th><th style="text-align: center; --cell-justify: center">$2$</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">$y$ </td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div></li><li><div class="list-item-paragraph">On the sheet of graph paper, using a scale of $2$cm to represent $1$ unit on the $x$-axis and $1$ cm to represent $1$ unit on the $y$-axis, draw the graph of the linear function $y=-2x+3$ for&nbsp;$-2\le x\le 2$.</div></li><li><div class="list-item-paragraph">From the graph, find the</div><ol class="i-list"><li><div class="list-item-paragraph">value of $y$ when&nbsp;$x=-\frac{1}{2}$ ,</div></li><li><div class="list-item-paragraph">the gradient of the equation $y=-2x+3$.</div></li></ol></li></ol>

<p>In the grid below, draw the graphs of  </p>
<ol class="i-list"><li><div class="list-item-paragraph">$y=2x-4$, for values of $x$ from $-4$ to $4$. </div></li><li><div class="list-item-paragraph">$y=4-5x$, for values of $x$ from $-2$ to $2$.  </div></li></ol>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1763745974436-dayu2x9dzc.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjM3NDU5NzQ0MzYtZGF5dTJ4OWR6Yy5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5Nzk2LCJleHAiOjE3OTI3MTAwOTZ9.Q9S573dydWrQjSD6LMCwwij02xHWfhxb6BcSrWXUtvA" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

Drawing Linear Graphs on Graph Paper

<p>In the grid below, draw the graphs of  </p>
<ol class="i-list"><li><div class="list-item-paragraph">$y=3x+1$</div></li><li><div class="list-item-paragraph">$y=-2x+3$</div></li></ol>
<p>for values of $x$ from $-4$ to $4$. </p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1763745574776-5bredkohfl.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjM3NDU1NzQ3NzYtNWJyZWRrb2hmbC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5Nzk2LCJleHAiOjE3OTI3MTAwOTZ9.Ow-YP4TOORr6mt1yIXRdLfZdwciueonCbDluDW2gziU" style="max-width: 400px; height: auto; display: block;" class="aligncenter custom-width" /></figure>

<ol class="i-list"><li><div class="list-item-paragraph">The equation of a function is $y=3x-2$. Complete the following table.</div><div class="table-container"><table style="table-layout: fixed; width: 400px;"><colgroup><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$x$</th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$-2$</th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$0$</th><th style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$y$</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$-2$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$10$</td></tr></tbody></table></div></li><li><div class="list-item-paragraph">In the grid below, draw the graph of $y=3x-2$ .  </div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1763745067766-jhxcrqrzbt.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjM3NDUwNjc3NjYtamh4Y3JxcnpidC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5Nzk2LCJleHAiOjE3OTI3MTAwOTZ9.nfPDED2Bnz90MQR0SSxTyaEy5I_di5UeAialHBd4IMg" alt="List item image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div></li></ol>

Completing a Table and Graphing a Linear Function

<ol class="i-list"><li><div class="list-item-paragraph">The equation of a function is $y=-2x+1$. Complete the following table.</div><div class="table-container"><table style="table-layout: fixed; width: 400px;"><colgroup><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$x$</th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$-2$</th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$0$</th><th style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$y$</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$1$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$2$</td></tr></tbody></table></div></li><li><div class="list-item-paragraph">In the grid below, draw the graph of $y=-2x+1$ .  </div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1763744605272-6d2zhoxarcw.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjM3NDQ2MDUyNzItNmQyemhveGFyY3cucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTc5NiwiZXhwIjoxNzkyNzEwMDk2fQ.goLdKmyxbAx7t8gbp60vuu3rYmS6eyiMPIG_8knnTTc" alt="List item image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div></li></ol>

<p>The grid below shows the triangle $PQR$.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1760432515782-v5tz02fow8.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjA0MzI1MTU3ODItdjV0ejAyZm93OC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5Nzk2LCJleHAiOjE3OTI3MTAwOTZ9.P73MKkQin9A3i1yeJCOKD34KGu9hH1BuqiAXrutlpFE" style="max-width: min(450px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-paragraph">State the gradient of the line $PQ$.</div></li><li><div class="list-item-paragraph">Find the gradient of the line $RQ$.</div></li><li><div class="list-item-paragraph">On the grid, draw and label the graph of $x=5$.</div></li><li><div class="list-item-paragraph">Write down the coordinates of $S$ such that&nbsp;$PQRS$ is a parallelogram.</div></li></ol>

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