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Year 10 Mathematics Worksheet 1
Functions
- For the relation ๐ฆ = 2 ๐ฅ + 1 , where ๐ฅ = โ 2 , โ 1 , 0 , 1 , list
(a) The range of the relation.
(b) The relation as a set of ordered pairs.
- The graph of a relation g is shown in the diagram given below.
y
-2 -1 0 1 2 3 x
(i) Find the value of ๐(โ 2 )
(ii) Solve for ๐ฅ if ๐
- Consider the graph shown below.
(a) What is the equation of line p
(b) Give the inequality of the shaded region.
- A relation is given as ๐ฆ = ๐ฅ + 1 , where ๐ฅ โ {โ 1 , 0 , 1 }
(i) List the range of this relation
(ii) List the ordered pairs of this relation
(iii) Is this relation a function? Give a reason for your answer.
- Line q is given below.
y
x
q
(i) Find the coordinate of y-intercept.
(ii) Find its gradient.
(iii) Determine the equation of line q
- A function f is defined as ๐(๐ฅ) = 3 ๐ฅ + 2
(i) Find the value of ๐
(ii) Solve for ๐ฅ if ๐(๐ฅ) = 3
- An inequality is given as ๐ฅ + 4 ๐ฆ โค 4.
(i) Find the x-intercept and y- intercept of the equation ๐ฅ + 4 ๐ฆ = 4.
(ii) Draw the inequality on a Cartesian plane.
- A line p passes through the point (โ 2 , 0 ) and ( 0 , 4 ).
(i) Draw line p on a Cartesian plane
(ii) Calculate the gradient of line p
(iii) Write the equation of line p in the form ๐ฆ = ๐๐ฅ + ๐.
- Four more than three times a number is equal to two times the number.
(i) Let the number be m and write an equation to represent ๐ฅ.
(ii) Solve the equation to find the value of ๐ฅ.
- r
h
The volume of the above cylinder is given by the formula V = r
2
h
(a) Make r the subject of the formula.
(b) Calculate the radius, r , of the cylinder if V = 50 cm
3
and h = 4 cm.
- If m = - 3, n = 2, p = - 1, find the value of:
(i) m n
(ii)
p
m + n
(iii) m
2
- n
2
- The area of a trapezium can be found using the formula
A =
h
(a + b)
(i) Make h the subject of the formula.
(ii) Find h if A = 20cm
2
, ๐ = 6 ๐๐ and ๐ = 4 ๐๐.
Year 10 Mathematics Worksheet 3
Numbers
- Simplify the following
(a) ( 2 ๐
3
2
(b) ๐ฅ
0
0
0
(c) 6 ๐ฅ
5
รท 3 ๐ฅ
2
(d) 3 ๐ฅ
2
ร ๐ฅ
(e)
โ 25
โ 36
(f) (
2 ๐
3
2
- (a) Express as a single power of p:
p
2
๏ด p
5
๏ธ p
3
(b) Simplify (3 x
4
2
0
- Using base as 2, write 8 in base index form
- Write in simplest base index form
(a) ๐ ร ๐ ร ๐ ร ๐ ร ๐ ร ๐
(b) 2 ร 2 ร ๐ฅ ร ๐ฅ ร ๐ฅ ร ๐ฆ ร ๐ฆ
- Evaluate
(a) 2
โ 3
(b) ( 2
3
2
(c) ( 3
6
3
รท 3
5
- In the diagram given below, XY is the diameter of the circle.
X
8cm
p
6cm
q
Z
Y
If XZ = 8cm and ZY = 6cm,
(i) calculate the length of the diameter of the circle.
(ii) find the value of angle p.
(iii) calculate the value of angle marked q.
- In the diagram O is the centre of the circle.
(i) Find the length marked x.
(ii) Find the radius of the circle.
- In the figure given below, chords AB and CD intersect outside the circle
at point X.
a) Complete the relationship: AX x _____ = _____ x DX
b) Find the length of CD
- A building is 5m away from a restaurant.
7m
h
5m
Find the height, h of the building. (Round off your answer to one
decimal place)
- A 5m ladder is leaning against a wall. The foot of the ladder is 1m out
from the wall.
5m
1m
Find the height, h which the ladder reaches up the wall.
- The diagram below shows a clinometer used to find the angle of elevation
of the top of a flagpole.
90
0
120
0
90ยฐ flagpole
What is the angle of elevation to the top of the flagpole?
Restaurant
Building
