Pixymaths Example GCSE Maths Questions and Answers

No. Grade Question
1EAngles - Q3
Calculate and write down the value of the letters x,y and z
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2A*Functions Using Quadratics - Q18
Sketch the graph of f(x) =  x2 + 2x 3.  On the same set of axes sketch:

(a) f(x ) + 2 (b) 2f(x)
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3CBGraphs (Quadratics and Cubics) - Q1
Complete the following table and hence draw the graph of y = x2 – 6x + 5.



Hence solve x2 – 6x + 5 = 0.
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4FTime - Q38
I need to catch the 1917 train. If I ring for a taxi and the taxi journey to the station takes 24 minutes, at what time do I need the taxi in order to arrive at the station with 5 minutes to spare?
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5BSpeed, Distance, Time - Q19
A swallow flies at a speed of 50 km/h for 3 hours and then a speed of 40 km/h for a further 2 hours. Find the average speed for the whole journey.
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6CProblems Requiring Equations - Q11
If 5 times a number is subtracted from 8 more than 7 times a number, the result is 24. Find the number.
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7CArea and Circumferance of Circles - Q24
A running track has two semi-circular ends of radius 28 m and two straight sides. The perimeter of the track is 400 m. Calculate a) the length of each curve and b) the length of each straight.
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8CBearings - Q26

a) What is the bearing of C from B?
b) What is the bearing of A from B?
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9CLocus - Q1
Draw the locus of the points that satisfy the given conditions:

(a) Points 3 cm from a given point.
(b) Points 1 cm from a given straight line, assumed to continue indefinitely in each direction.
(c) Points equidistant from two fixed points, C and D, where CD = 4 cm.
(d) Points equidistant from two straight lines EF and EG.
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10A*Sine & Cosine Graphs - Q4
Draw the graph of y = 2 – sin 1/2 x, for 0° ≤ x ≤ 360°.

When x = 60°, y = 11/2 . What is the other value of x for which y = 11/2 ?
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11ESymmetry - Q31
Copy and complete the shapes so that the two black lines are the axes of symmetry. The shape is in blue.

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12CTransformations - Q18
Draw the triangle with the following coordinates:- (3, 1), (8, 5), (10, 2).

(a) Using (0,0) as the centre of rotation, rotate it through 90° anticlockwise.
(b) Rotate this new image 90° clockwise, using (1, 4) as the centre of rotation.
(c) What transformation maps the original triangle directly on to the answer to part (b)?
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13CTime Distance Graphs - Q5
The following graph shows a journey:



(a)  How far was the cyclist from home after (i) 45 min (ii) 1 hr 15 min (iii) 1 hr 30 min?
(b) The cyclist’s first stop was at Dorton.
      (i) How far is Dorton from the cyclist’s home?
      (ii) For how long did he stop at Dorton?
(c)  What was the cyclist’s average speed
      (i) from home to Dorton?
      (ii) from Dorton to the end of his journey?
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14A*Vectors - Q1

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15BTrigonometry - Q64
An aircraft flies 400 km from a point O on a bearing of 025° and then 700 km on a bearing of 080° to arrive at B.

(a) How far north of O is B?
(b) How far east of O is B?
(c) Find the distance and bearing of B from O.
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16BCumulative Frequency Graphs - Q14
Draw a cumulative frequency curve for the following distribution of ages of workers in a factory:-



(a)     Which is the modal class?
(b)     What is the interquartile range?
(c)     What is the probability that a worker chosen at random will be 30 or more?
(d)     What is the probability that a worker chosen at random will be in the top two class intervals?
(e)     Estimate the median.
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17AHistograms - Q12
The following table and histogram show the daily takings of a shop over a period of time.  Fill in the missing entries in the table and the missing bars on the histogram.


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18Dpie Charts - Q18


The bar chart above shows the number of different milk shakes sold in an hour.  Draw a pie chart to show the information.
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19DProbability using tables - Q4


200 men and women were asked which of two political parties, A or B, they would vote for.  The results are shown in the table above. Complete it and answer the following questions.

(a) What is the probability that a woman selected at random would vote for Party B?
(b)  What is the probability that a man selected at random would not know which Party he would vote for?
(c)  What is the probability that a person selected at random is a woman who would vote for Party A?
(d)  What is the probability that a person selected at random from those who don’t know which Party they would vote for is a man?
(e)  What is the probability that a person selected at random would vote for Party B?
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20CScatter Graphs - Q8
The following table shows the ages and blood pressure of a group of women:



(a) Draw a scatter diagram to depict this information with the age along the horizontal axis and the blood pressure up the vertical axis.
(b) Draw in a line of best fit.
(c) Use your graph to predict the blood pressure of a woman aged 65.
(d) Use your graph to predict the age of a woman whose blood pressure is 125.
(e) Describe the trend and explain what this means.
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