Question 1:
1 (a)
Draw a line through point P that is perpendicular to line l.
(b) Write down the mathematical names for two different quadrilaterals with
• two lines of symmetry
and
• rotational symmetry of order two.
………………………………… and ………………………………….
(c) The diagram shows a quadrilateral on a $1cm^{2}$ grid.
Find the area of this quadrilateral.
…………………………………… cm $^{2}$
(d)
The diagram shows a quadrilateral DEFG and a straight line FGH.
(i) Angle DEF = 82°.
Write down the mathematical name for this type of angle.
(ii) Work out the value of x.
Give a geometrical reason for your answer.
x = …………………….. because …………………………………………………….
(iii) Work out the value of y.
Give a geometrical reason for your answer.
y = …………………….. because …………………………………………………….
▶️Answer/Explanation
Ans :
1(a) Ruled line drawn through P,
perpendicular to l.
1(b) rectangle rhombus
1(c) 11
1(d)(i) acute
1(d)(ii) 37
Angles on a straight line add to 180
1(d)(iii) 32
Angles in a quadrilateral add to 360
Question 2:
(a)
(i) Tiya buys 55 litres of fuel from garage A. Work out the change she receives from $100$.
(ii) Work out how much cheaper it is to buy 20 litres of fuel from garage A than from garage B.
(iii) These are the amounts that 6 people spend on fuel at garage A.
$63$ $84.50$ $72.23$ $46$ $54.10 $ $80$
Calculate the mean number of litres that they buy.
………………………………….. litres
(iv) The cost of fuel at garage B increases from $1.50$ to $1.53$ .
Calculate the percentage increase.
……………………………………….%
(b) The fuel tank of a car is $\frac{2}{5}$ full.
It takes 39 more litres of fuel to fill the tank.
Work out the number of litres of fuel in a full tank.
………………………………….. litres
(c) (i) Use 1 litre = 0 2. 2 gallons to complete this conversion graph.
(ii) Use 1 litre = 0 2. 2 gallons to complete this statement.
1 gallon = ………………………… litres.
(d) A cylindrical tank for storing fuel has radius 1.5 metres and height 8 metres.
Calculate the volume of the tank in litres.
………………………………….. litres
▶️Answer/Explanation
Ans :
2(a)(i) 22.45
2(a)(ii) 1.8[0]
2(a)(iii) 47.3 or 47.26…
2(a)(iv) 2
2(b) 65
2(c)(i) A straight line through (0,0) and (100,22)
2(c)(ii) 4.55 or 4.545
2(d) 56500, 56600 or 56540 to 56560…..
Question 3:
3 (a) In triangle DEF, DE = 6 cm and DF = 4 8. cm.
Using a ruler and compasses only, construct triangle DEF.
Leave in your construction arcs.
The line EF has been drawn for you.
(b)
(i) Write down the letter of the triangle that is congruent to triangle T.
(ii) Write down the letter of the triangle that is similar but not congruent to triangle T.
(c)
The diagram shows an isosceles triangle.
(i) Show that the perpendicular height, h, is 6.58cm, correct to 3 significant figures.
(ii) Calculate the area of the triangle. Give the units of your answer.
(iii) Kalpit tries to arrange some of these triangles to make a regular polygon with centre O.
Show that Kalpit cannot make a regular polygon.
▶️Answer/Explanation
Ans :
3(a) Correct triangle drawn with construction arcs.
3(b)(i) G
3(b)(ii) F
3(c)(i) [h=]
$\frac{7}{2}$ tan 62 oe
6.582 to 6.583
3(c)(ii) 23[.0] or 23.03 to 23.04…
cm$^{2}$
3(c)(iii) $\frac{360}{180-2\times 62}$
6.4… which is not integer oe
Question 4:
4 (a) A shop sells 58 televisions in one week.
The bar chart shows the number of televisions that the shop sells on five of the days.
(i) Write down the number of televisions that the shop sells on Monday.
(ii) Find the fraction of the televisions that the shop sells on Sunday.
(iii) The number of televisions that the shop sells on the other two days is in the ratio
Wednesday : Friday = 2 : 3.
Complete the bar chart.
(iv) Write down the mode.
(b) A television has a price of $550.
This price is reduced by 4%.
Calculate the new price of this television.
(c) The scatter diagram shows the prices of different sized televisions.
Write down the type of correlation shown in the scatter diagram.
(d) Hemang buys two televisions.
The probability that a television is faulty is 0.02 .
(i) Complete the tree diagram.
(ii) Find the probability that Hemang buys two faulty televisions.
(iii) The shop sells 4150 televisions in one year.
Calculate the expected number of faulty televisions.
▶️Answer/Explanation
Ans :
4(a)(i) 3
4(a)(ii) $\frac{11}{58}cao$
4(a)(iii) Completely correct bar chart
4(a)(iv) Saturday
4(b) 528
4(c) Positive
4(d)(i) 0.02
0.98
0.98 0.02
0.98 oe
4(d)(ii) 0.0004 oe
4(d)(iii) 83
Question 5:
5 (a) (i) Complete the table of values for $y =-x^{2}+5x+7$ .
(ii) On the grid, draw the graph of $y =-x^{2}+5x+7$ for $-1\leq x\leq 6$.
(iii) (a) Write down the equation of the line of symmetry of the graph.
(b) The points ( – 8 , – 97) and ( t ,-97) also lie on the graph of $y=-x^{2}+5x+7$ .
Use symmetry to find the value of t.
t = ………………………………………….
(b) Write down the gradient of the line y = 9x- 4.
(c) Write down the equation of a line parallel toy x =-5 x+1 9.
y = ………………………………………….
(d)
Find the equation of line L in the form y= mx+ c.
y = ………………………………………….
(e) Make x the subject of the formula y = mx+ c.
x = ………………………………………….
▶️Answer/Explanatioy m = +x c.
Ans :
5(a)(i) 1, 7, 13, 13, 7
5(a)(ii) Completely correct curve
5(a)(iii)(a) x = 2.5 oe
5(a)(iii)(b) 13
5(b) 9
5(c) y=-5x+k = where k ≠19
5(d) $\left [ x= \right ]\frac{y-c}{m}oe$ final answer
Question 6:
6 (a) Town S is 44km from town R on a bearing of 117°.
(i) Using a scale of 1 cm represents 8km, mark the position of town S.
Scale: 1cm to 8km
(ii) Anvi cycles the 44km from R to S.
She leaves R at 1315 and cycles at a speed of 12km/h.
Work out the time she arrives at S.
(b) A tower has a height of 16 metres.
When Jai makes a scale drawing of the tower it has a height of 20cm.
Work out the scale Jai uses, giving your answer in the form 1 : n.
1 : ………………………………………….
(c) X, Y and Z are three towns.
X is on a bearing of 288° from Y.
Z is on a bearing of 018° from Y.
(i) Show that angle XYZ is 90°.
(ii) XY = 6 km and YZ = 9 7. km.
Calculate XZ.
XZ = …………………………………….. km
▶️Answer/Explanation
Ans :
6(a)(i) The position of S correctly marked on the diagram
6(a)(ii) 16 55
6(b) [1:]80
6(c)(i) 360-288+18 oe
6(c)(ii) 11.4 or 11.40 to 11.41
Question 7:
7 (a) P= 3a+ 5
Find the value of P when a = 2.
P = …………………………….
(b) Solve these equations.
(i) 7x=-4 2
x = ……………………………..
(ii) 9(8-7x ) = 72
x = ………………………………
(c) 5$^{8}$×5 $^{2}$ $^{-24}$
Find the value of k.
k = ………………………………………….
(d) Solve the simultaneous equations.
-6x-y=13
8x+y=-51
x = ………………………………………….
y = ………………………………………….
(e) n is an integer where n >-3 and n $\leqslant $ 1.
Write down all the possible values of n.
(f) A boy walks for 35 minutes at x metres per minute.
He then runs for t minutes at 160 metres per minute.
Write down an expression, in terms of x and t, for the total distance, in metres, the boy travels.
………………………………………. m
(g)
Find an expression for the area of this rectangle.
Give your answer in the form $x^{2}+ax+b$.
▶️Answer/Explanation
Ans :
7(a) 11
7(b)(i) −6
7(b)(ii) 1.875 oe
7(c) −32
7(d) $\left [ x= \right ]-19 \left [ y= \right ]101$
7(e) −2, −1, 0, 1
7(f) 35 160 x t + final answer
7(g) x$^{2}$+3 x−10 final answer
Question 8:
8 (a) 120 people teach in a university mathematics department.
Some information is shown in the table.
One fifth of the people are professors.
30% of the people are part-time.
Work out the number of full-time lecturers.
$\xi$= {children in a school}
F = {children who like fruit}
V = {children who like vegetables}
24 children like vegetables but do not like fruit.
8 children do not like fruit and do not like vegetables.
$n\left ( F\bigcap V \right )=9$
n (F) = 3×n(V )
(i) Complete the Venn diagram. [3]
(ii) Work out n(F UV)
▶️Answer/Explanation
Ans :
8(a) 71 nfww
8(b) (i)
8(b)(ii) 123