Mathematics · WJEC 3300 · Unit 2: Calculator-allowed · Higher · November 2023
The table below shows some of the values of y = x2 + 4x + 5 for values of x from –4 to 1.
| x | –4 | –3 | –2 | –1 | 0 | 1 |
| y = x2 + 4x + 5 | 5 | 2 | 2 | 5 |
Complete the table by finding the value of y for x 
–2 and for x 
1.
[2]
On the graph paper below, draw the graph of y = x2 + 4x + 5 for values of x
from –4 to 1.
[2]
Find the volume of the solid prism shown above.
[3]
The solid prism is made of gold. Gold has a density of 19∙3 g/cm3. Calculate the mass of the prism.
Give your answer in kilograms.
[3]
A solution of the equation
lies between 3 and 4.
Use the method of trial and improvement to find this solution correct to 1 decimal place.
You must show all your working.
[4]
7 cubes are stacked on top of each other. Each of these cubes has edges of length 60 mm, measured correct to the nearest millimetre.
Calculate the greatest possible height of this stack of 7 cubes.
[2]
The grouped frequency table below shows data for 32 values of t. One of the frequencies in the table is represented by a.
| t | Frequency |
20  t  30 | 2 |
30  t  40 | 8 |
40  t  50 | 4 |
50  t  60 | a |
| 60 t 70 | 3 |
70  t  80 | 5 |
Find the estimated mean value of t for the 32 values.
[5]
Factorise 6x2 +19x +10.
[2]
Fully factorise the expression m3 − 25m.
[3]
Factorise (p + 7)(p + 29) + 2(p + 7).
[2]
A solid has a height of 225 cm.
A larger, mathematically similar solid has a height of 855 cm. The surface area of the smaller solid is 5300 cm2.
Calculate the surface area of the larger solid.
[3]
The values b = 23, c = 0·73 and d = 8·3 are each given correct to 2 significant figures.
Use the formula
to calculate the greatest possible value of a. Give your answer correct to 2 decimal places.
You must show all your working.
[3]
Put a tick next to the graph that represents the equation y =−x3.
[1]
Use the axes below to sketch the graph of y =− 
[2]
Calculate the probability that every child passes their ball to the left.
[2]
Calculate the probability that one of the three children does not receive a ball.
[3]
Calculate the length of CE.
You must show all your working.
[6]
Hence, calculate the area of triangle CGE.
[2]
Use the quadratic formula to solve the equation 
+ 5 = 7x.
Give your answers as decimal numbers.
You must show all your working.
[5]
The paper as printed
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