IB MATH STUDIES SL 1: IB-Style Review Questions for Test
Linear and Simultaneous Equations, Linear Relations, and Functions
1.
A quadratic function, f(x) = ax2 + bx, is represented by the mapping diagram below.
(a)
Use the mapping diagram to write down two equations in terms of a and b.
(2)
(b)
Find the value of
(i)
a;
(ii)
b.
(2)
(Total 4 marks)
2.
A and B are points on a straight line as shown on the graph below.
(a)
Write down the y-intercept of the line AB.
(1)
(b)
Calculate the gradient of the line AB.
(2)
(Total 3 marks)
1
3.
The following diagram shows the lines l1 and l2, which are perpendicular to each other.
Diagram not to scale
y
(0, 7)
l2
(0, –2)
x
(5, 0)
l1
(a)
Calculate the gradient of line l1.
(b)
Write the equation of line l1 in the form ax + by + d = 0 where a, b and d are integers, and
a > 0.
(Total 8 marks)
4.
The line L1 shown on the set of axes below has equation 3x + 4y = 24. L1 cuts the x-axis at A
and cuts the y-axis at B.
Diagram not drawn to scale
y
L1
B
L2
M
O
A
x
C
(a)
Write down the coordinates of A and B.
(2)
M is the midpoint of the line segment [AB].
(b)
Write down the coordinates of M.
(2)
The line L2 passes through the point M and the point C (0, –2).
(c)
Write down the equation of L2.
(2)
(d)
Find the length of AC.
(2)
(Total 10 marks)
2
5.
The diagram shows triangle ABC. Point C has coordinates (4, 7) and the equation of the line AB
is x + 2y = 8.
diagram not to scale
(a)
Find the coordinates of
(i)
A;
(ii)
B.
(2)
(b)
Show that the distance between A and B is 8.94 correct to 3 significant figures.
(2)
N lies on the line AB. The line CN is perpendicular to the line AB.
(c)
Find
(i)
the gradient of CN ;
(ii)
the equation of CN.
(5)
(d)
Calculate the coordinates of N.
(3)
(Total 12 marks)
6.
P (4, 1) and Q (0, –5) are points on the coordinate plane.
(a)
Determine the
(i)
coordinates of M, the midpoint of P and Q;
(ii)
gradient of the line drawn through P and Q;
(iii)
gradient of the line drawn through M, perpendicular to PQ.
The perpendicular line drawn through M meets the y-axis at R (0, k).
(b)
Find k.
(Total 6 marks)
3
7.
Three points A (1, 3), B (4, 10) and C (7, –1) are joined to form a triangle. The
mid-point of AB is D and the mid-point of AC is E.
(a)
Plot the points A, B, C, on the grid.
(b)
Find the distance DE.
(Total 6 marks)
8.
f
4
A
5
1
–1
2
–2
–3
3
0
1
4
9
16
B
0
The diagram shows a function f, mapping members of set A to members of set B.
(a)
(i)
Using set notation, write down all members of the domain of f.
(ii)
Using set notation, write down all members of the range of f.
(iii)
Write down the equation of the function f.
The equation of a function g is g(x) = x2 +1. The domain of g is
(b)
.
Write down the range of g.
(Total 6 marks)
4
9.
The vertices of quadrilateral ABCD as shown in the diagram are A (3, 1), B (0, 2), C (–2, 1) and
D (–1, –1).
(a)
Calculate the gradient of line CD.
(2)
(b)
Show that line AD is perpendicular to line CD.
(2)
(c)
Find the equation of line CD. Give your answer in the form ax + by = c
where a, b, c  .
(3)
Lines AB and CD intersect at point E. The equation of line AB is x + 3y = 6.
(d)
Find the coordinates of E.
(2)
(e)
Find the distance between A and D.
(2)
(Total 11 marks)
10.
A is the point (2, 3), and B is the point (4, 9).
(a)
Find the gradient of the line segment [AB].
(b)
Find the gradient of a line perpendicular to the line segment [AB].
(c)
The line 2x + by – 12 = 0 is perpendicular to the line segment [AB]. What is the value
of b?
(Total 4 marks)
5
11.
The graph below shows part of the function y = 2 sin x + 3.
y
6
5
4
3
2
1
0
0º
90º
180º
270º
360º
450º
(a)
Write the domain of the part of the function shown on the graph.
(b)
Write the range of the part of the function shown on the graph.
x
(Total 4 marks)
12.
The diagram below shows the line PQ, whose equation is x + 2y = 12. The line intercepts the
axes at P and Q respectively.
diagram not to scale
(a)
Find the coordinates of P and of Q.
(3)
(b)
A second line with equation x – y = 3 intersects the line PQ at the point A. Find the
coordinates of A.
(3)
(Total 6 marks)
13.
The mid-point, M, of the line joining A(s, 8) to B(−2, t) has coordinates M(2, 3).
(a)
Calculate the values of s and t.
(2)
(b)
Find the equation of the straight line perpendicular to AB, passing through
the point M.
(4)
(Total 6 marks)
6
14.
The diagram shows the straight lines L1 and L2. The equation of L2 is y = x.
(a)
Find
(i)
the gradient of L1;
(ii)
the equation of L1.
(3)
(b) Find the area of the shaded triangle.
(3)
(Total 6 marks)
15.
The equation of a line l1 is y =
(a)
1
x.
2
On the grid, draw and label the line l1.
y
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 x
The line l2 has the same gradient as l1, but crosses the y-axis at 3.
(b)
What is the geometric relationship between l1 and l2?
(c)
Write down the equation of l2.
(d)
On the same grid as in part (a), draw the line l2.
(Total 4 marks)
7
16.
The following diagram shows the points P, Q and M. M is the midpoint of [PQ].
y
P(0, 2)
M
0
x
Q(2, 0)
(a)
Write down the equation of the line (PQ).
(b)
Write down the equation of the line through M which is perpendicular to the line (PQ).
(Total 4 marks)
17.
The following diagram shows a straight line l.
y
l
10
8
6
4
2
0
x
0
1
2
3
4
5
6
(a)
Find the equation of the line l.
(b)
The line n is parallel to l and passes through the point (0, 8). Write down the equation of
the line n.
(c)
The line n crosses the horizontal axis at the point P. Find the coordinates of P.
(Total 4 marks)
8
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REVIEW TEST IB QUESTIONS SOLUTIONS Linear