National 5 Maths Expressions and Formula
Practice Test B
Some questions are marked (A/B). These questions are more difficult than the unit assessment, and can be missed out if you are not confident with them.
Formulae you get given in the test
Volume of a sphereVolume of a cone
1a.b. / Simplify, giving your answer in surd form:
(A/B) Hence simplify
2a. / Simplify:
(i) / / (ii) /
(iii) / / (iv) /
2b. / The number of millimetres in one mile is 1·609 × 106.
Calculate the number of millimetres in 26 miles. Give your answer in scientific notation.
3 / Expand and simplify where appropriate:
a. / b.
c. (A/B) / d.
4. / Factorise:
a. / b.
c. / d.
e. (A/B) / f. (A/B)
5. / Express in the form
6. / Write:
in its simplest form.
7. / Points P and Q have coordinates (–9, –1) and (6, 4) respectively.
Calculate the gradient of PQ
8. / Write each of the following as a single fraction:
a. / b.
c. / d. (A/B)
9. / Calculate the volume of a cone with radius 14·4mm and height 24mm,
giving your answer correct to three significant figures.
10. / Marc is designing cardboard
party hats for a P1 Christmas party.
In the diagram the shaded area
represents the cardboard used
for one of these hats.
- XY is a minor arc of the circle
- The radius OS is 14 cm.
- Angle XOY is 165°.
a.Calculate the area of the minor sector OXY.
b.Marchas 3000cm² of cardboard. What is the maximum number of hats that he could make with this material? Show all working clearly.
11. / (A/B) A cone has a volume of 400cm³ and a diameter of 8cm. Calculate the height of the cone.
12. / (A/B) A fan has four identical blades. Each blade is a sector of a circle with radius 5cm and the angle at the centre of each circle is 64°. Calculate the total area of plastic required to make the blades.