Probability
Trigonometry
Logarithms
Data Analysis
Linear and Non linear equations
100
A letter is selected randomly from the alphabet. Find the probability that it is a vowel or Y.
P(Vowel or y)=6/26 = 3/13
100
Find the value of a.
10 √3
100
Evaluate Log99
1
100
The heights in centimetres of a group of Ballet dancers are:
165 183 170 168 175 179 168 170 181 168 172 177 171 170 175 179
Calculate the mean, correct to one decimal place.
173.2 cm
100
solve 2(5+4x)=6(x-2)
x=-17
200
If Sandy has a 68% chance of missing a basketball shot, what is the probability that she scores with the shot?
32%
200
A playground slide of length 8 metres makes an angle of 55° with the horizontal. Find the height of the top of the slide above the ground, to two decimal places.
6.55 metres
200
Solve loga16 + loga3 - loga2
Loga24
200
For quality testing, a manufacturer takes a random sample of 10 screws, each designed to have a length of 2 cm. The actual lengths of the screws, in centimetres, are:
2.00 1.99 1.98 2.01 2.01 1.97 2.03 1.98 2.01 2.00
Find the standard deviation, correct to two decimal places.
0.02 cm
200
Is x = y2 + 7 a function? give reasons for your answer.
No as it does not pass the vertical line test - there are multiple y values for each x value.
300
A bag contains 3 blue marbles and 5 green marbles. Two marbles are drawn without replacement. What is the probability that they will be the same colour?
P (same colour) = 13/28
300
Find the length of AC, to one decimal place
16.93 units
300
Solve 2x+1 = 8
x=2
300
Use the scatterplot and line of best fit to predict the value of y when x = 10.
y = 35
300
solve
9x^2 + 3x − 12=0
x=-4/3, x=1
400
For three children, there are possible combinations of boys (B) and girls (G). If a three child family is selected at random, what is the probability that it contains exactly one boy?
P(1 boy)=3/8
400
Find the area of this triangle.
167 cm2
400
Solve for 5logx
1/x
-5
400
Find the equation of a line of best fit if it is known that it passes through the points (5, 5) and (20, 27).
y=22/15 x - 7/3
400
Solve the following simultaneous equations:
y=x^2+3x-4
y=3x+5
x=-3, y=-3
x=4,y=2
500
Tegan buys 5 tickets in a raffle which 80 tickets are sold. There are three prizes. Use a tree diagram to find the probability that Tegan wins at least one prize.
17%
500
Boolean (B) is 34 km S 46° W of Axiom (A). Pascal (P) is 27 km due north of Boolean.
Calculate the distance from Pascal to Axiom.
24.7 km
500
Simplify the following expression: Log5(625/25)
2
500
Mr MacDonald recorded the test marks for his Year 10 class of 25 students. He calculated the average mark to be 72. Sandra’s mark of 86 was incorrectly marked as 36. What was the correct average mark for the test?
74
500
Kristina spent 1/4 of her money, then she spent 1/4 of the remainder. All together she spend $126. How much money did she have to start with?
$288