Grade 11 – Baseline worksheet
1)
1)
60𝑜
60𝑜
2)
3)
4) Show that
5)
6)
√20+√80
√3
can be expressed in the form of √𝑎 where a is an integer.
[3]
7)
8)
57.7 has been rounded to 1 decimal place. Work out the upper and lower bounds (or
error interval) of this value.
[2]
9)
10) A vehicle drives at 45 km/h for 5 hours before deciding to slow down to 40 km/h for
the next 2 hours. Calculate the average speed using the formula for average speed. [2]
11) A marble rolls 5.2 m in 1.8 s. What was the marble's average speed?
[1]
12) Phillip walks along a straight path from his house to his school. How long will it take
him to get to school if he walks 428 m west with an average velocity of 1.7 m/s west?
[2]
13)
3
Simplify 82 × √46
Give your answer in the form 2𝑎 where 𝑎 is an integer.
Show each stage of your working.
14)
[3]
𝑥
If 𝑓(𝑥) = (2 − 𝑥)3 , and 4𝑛 = 𝑓(10), then what is the value of 𝑛?
15) Simplify the following.
a.
(4𝑥𝑦 −2 )(−12𝑥 −4 𝑦12 )
6𝑥 2 𝑦
[2]
16)
Simplify the below equation
1
1
1
+
+
𝑎−𝑏
𝑎−𝑐
𝑏−𝑐
𝑏−𝑎
𝑐−𝑎
1+𝑥
+𝑥
1+𝑥
+𝑥
1+𝑥
+ 𝑥 𝑐−𝑏
17)
[3]
18)
A chord subtends an angle of 90𝑜 at the centre of a circle whose radius is 20 𝑐𝑚.
Compute the area of the corresponding major segment of the circle.
19)
Area of a sector of a circle of radius 36 𝑐𝑚 is 54𝜋 𝑐𝑚2 . Find the length of the
corresponding arc of the sector.
20)
The cross – section of a gate is a sector of a circle with radius 8.5 𝑚 and angle 76𝑜 .
Calculate the perimeter of the sector.
[3]
21)
A class of 24 students have a mean height of 1.56 meters. Two new students join the
class and the mean height of the class increases to 1.58 meters. Given that the two
new students are of equal height, find their height.
22)
The test scores of 14 students are shown below.
21 21 23 26 25 21 22 20 21 23
Find the range, mode, median and mean of the test scores
23
27
24
21
23)
Shahruk plays four games of golf. His four scores have a mean of 75, a mode of 78
and a median of 77. Work out his four scores.
[3]
24)
𝐴𝐵𝐷𝐹 is a parallelogram (as shown below) and 𝐵𝐶𝐷𝐸 is a straight line. 𝐴𝐹 =
12𝑐𝑚, 𝐴𝐵 = 9𝑐𝑚, and angle 𝐶𝐹𝐷 = 40𝑜 and angle 𝐹𝐷𝐸 = 80𝑜 . Calculate the height
ℎ, of the parallelogram.
25)
The straight line 𝐴𝐶 has equation 𝑦 = 4𝑥 + 5.
Calculate the acute angle between 𝐴𝐶 and and the 𝑥 – axis.
[2]
26)
The sun shines on a flagpole, causing a shadow to be cast on the ground. The distance
from the base of the pole to the tip of the shadow is 49 feet. At that time of day, the
sun’s rays make an angle of 38 with the ground. How tall is the flagpole?
[2]
27)
[5]
28)
The equation of line 𝐿 is 3𝑥 − 8𝑦 + 20 = 0
a. Find the gradient of line 𝐿.
b. Find the coordinates of the point where line 𝐿 cuts the 𝑦- axis.
29)
A rhombus 𝐴𝐵𝐶𝐷 has a diagonal 𝐴𝐶 where 𝐴 is the point (−3,10) and 𝐶 is the point
(4, −4)
a. Calculate the length 𝐴𝐶.
[3]
b. Show that the equation of the line 𝐴𝐶 is 𝑦 = −2𝑥 + 4
[2]
30)
The solution of the equation 𝑥 2 + 𝑏𝑥 + 𝑐 = 0 are
Find the value of 𝑏 and the value of 𝑐.
−7+√61
2
and
−7−√61
2
.
[3]
31) The diagram shows a sketch of the curve 𝑦 = 𝑥 2 + 3𝑥 − 4.
Find the coordinates of the points 𝐴, 𝐵 and 𝐶.
[4]
5
𝑥−5
3𝑥+8
32) Solve the equation 2−𝑥 + 𝑥+2 + 𝑥 2−4 = 0.
33)
34)
35)
36)
37)
38)
39)
40)
41)
Expand using identities and simplify.
42)
43)
44)