Home / Practice / Algebra and data analysis / Worksheet

Algebra and data analysis

Written by Hassan Raza (Mathematics)

SAT for LUMS · Mathematics · 26 questions

Name: ____________________ Date: ____________

If 3x + 5 = 20, what is the value of x?
- A 15
- B 5
- C 3
- D 25/3
The line y = 2x + 3 crosses the y-axis at the point:
- A (0, 2)
- B (3, 0)
- C (2, 3)
- D (0, 3)
If x + y = 10 and x − y = 2, what is x?
- A 8
- B 12
- C 6
- D 4
If f(x) = x² − 4x + 3, what is f(5)?
- A 12
- B 8
- C 3
- D 18
The mean of 5 numbers is 12. When one of the numbers, 20, is removed, what is the mean of the remaining 4?
- A 8
- B 10
- C 15
- D 12
A price increases from 40 to 50. What is the percent increase?
- A 20%
- B 25%
- C 10%
- D 50%
What are the solutions of x² − 7x + 12 = 0?
- A 2 and 6
- B 3 and 4
- C −3 and −4
- D 1 and 12
What is the median of 3, 7, 8, 12 and 15?
- A 9
- B 12
- C 8
- D 7
A line is parallel to y = 3x − 1 and passes through (0, 4). What is its equation?
- A y = −3x + 4
- B y = 3x − 4
- C y = x/3 + 4
- D y = 3x + 4
A population of 100 bacteria doubles every 3 days. How many are there after 9 days?
- A 900
- B 300
- C 800
- D 600
If 2(x + 3) = 14, what is the value of x?
- A 11
- B 7
- C 4
- D 8
If 2x + y = 11 and x − y = 1, what is the value of x?
- A 4
- B 3
- C 5
- D 6
If f(x) = 3x − 2, what is f(4)?
- A 14
- B 12
- C 6
- D 10
What are the solutions of x² + 2x − 15 = 0?
- A −3 and 5
- B 5 and 3
- C 15 and −1
- D 3 and −5
30 is 20 percent of what number?
- A 600
- B 6
- C 60
- D 150
What is the mean of 6, 8, 10 and 12?
- A 8
- B 10
- C 9
- D 40
Every value in a data set is increased by 5. By how much does the mean increase?
- A It cannot be known
- B 5
- C 0
- D 25
A line passes through (0, −1) and has slope 4. What is its equation?
- A y = 4x + 1
- B y = x/4 − 1
- C y = 4x − 1
- D y = −x + 4
A balance of 200 grows by 10 percent each year. What is it after 2 years?
- A 240
- B 220
- C 242
- D 222
Which values of x satisfy 3x − 5 > 10?
- A x > 3
- B x > 5
- C x > 15
- D x < 5
Three pencils cost Rs 45. How much do 8 pencils cost at the same rate?
- A Rs 90
- B Rs 120
- C Rs 105
- D Rs 135
A bag has 3 red and 5 blue marbles. One marble is picked at random. What is the probability that it is red?
- A 1/3
- B 5/8
- C 3/5
- D 3/8
What is the median of 2, 5, 7, 9, 12 and 14?
- A 8
- B 7.5
- C 7
- D 9
If x² = 49 and x < 0, what is x?
- A −7
- B −3.5
- C −49
- D 7
A cyclist travels 150 km in 2.5 hours. What is the average speed?
- A 65 km/h
- B 375 km/h
- C 50 km/h
- D 60 km/h
If g(x) = x² + 1, what is g(−3)?
- A −8
- B −10
- C 10
- D 8

Answer key

1. B, 2. D, 3. C, 4. B, 5. B, 6. B, 7. B, 8. C, 9. D, 10. C, 11. C, 12. A, 13. D, 14. D, 15. D, 16. C, 17. B, 18. C, 19. C, 20. B, 21. B, 22. D, 23. A, 24. A, 25. D, 26. C

Subtract 5 to get 3x = 15, then divide by 3.
The y-intercept is the constant term, 3.
Adding the equations gives 2x = 12, so x = 6.
f(5) = 25 − 20 + 3 = 8.
The total is 60, so the remaining total is 40, and 40 ÷ 4 = 10.
The increase is 10 on 40, which is 25%.
The equation factors as (x − 3)(x − 4) = 0.
The middle number of the ordered list is 8.
Parallel lines have the same slope, and the y-intercept is 4.
9 days is 3 doublings: 100 × 2 × 2 × 2 = 800.
Divide by 2 to get x + 3 = 7, so x = 4.
Adding the equations gives 3x = 12, so x = 4.
f(4) = 12 − 2 = 10.
The equation factors as (x − 3)(x + 5) = 0.
30 ÷ 0.2 = 150.
The sum is 36 and 36 ÷ 4 = 9.
Adding a constant to each value adds the same constant to the mean.
The y-intercept is −1 and the slope is 4.
200 × 1.1 × 1.1 = 242.
3x > 15, so x > 5.
One pencil costs Rs 15, so 8 cost Rs 120.
There are 3 red marbles out of 8.
The middle two values are 7 and 9, and their mean is 8.
The square root of 49 is 7, and x must be negative.
Speed = 150 ÷ 2.5 = 60.
g(−3) = 9 + 1 = 10.