IB Math SL 11
Name:
Summer Assignment - 2013
SHOW ALL WORK
Part 1 – Non-Calculator
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1. From the set {−8, −5.2, −√3, − 2, 0, √2, 2,  , 5.6666…, 9}, list the numbers that belong to the
following sets.
(a) Natural numbers
(c) Rational numbers
(e) Nonpositive integers
(g) ℚ
(b) Irrational numbers
(d) Negative integers
(f) ℕ
(h) ℤ_+
2. Decide whether each statement is true or false.
(a)
(b)
(c)
(d)
Every natural number is an integer.
Every real number is a rational number.
Every rational number can be written as a quotient of integers.
Some integers are rational numbers.
3. Evaluate the following.
(a) |6|
(b) −|−√3|
(d) |7| + |−8|
(c) |−(6 − 9)|
(e) |−10| − |2|
4. Express each number in the form 𝑎 × 10𝑘 , 1 ≤ 𝑎 < 10, 𝑘 ∈ ℤ (scientific notation).
(a) 89, 023,000
(c) 783.01 × 105
(b) 0.00523
5. Write each number in standard form.
(a) 1.50 × 107
(b) 1.62 × 10−4
(c) 10−6
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6. Express each number to 2 significant figures (s.f.).
(a) 8728
(b) 547000
(c) 0.0687
(b) 5 significant figures
(c) 5 decimal places
7. Express 3.141593 correct to:
(a) 4 significant figures
8. Evaluate the following expressions.
(a) 2(3 + 4 x 7)
(b) 24  4  3
(d) (1.2)(0.8)
(e) (0.2)2(1000)
3  15 
 2 1
(g) 4   7    
5  12 
 3 2
(c)
6(13  7  6)
28
(f)
3 6 2
  
2 4 3
2
2
(h) 5
3
(i)
4
3
5
9. Evaluate the following expressions.
(a) 23
(b) (−3)3
(e) 4−3
(c) −(5)2
(d) −24
1
2 −3
4
(g) 643
(f) (3)
(h) 273
10. Simplify. Use only positive exponents in the answer.
(a)
(d)
18𝑥 3 𝑦
12𝑥 2 𝑦 4
(𝑥 5 𝑦)
(b) 𝑝𝑞 4 (𝑝−8 𝑞 5 )−2
−1
𝑥 2 𝑦 −7
(e) (
4𝑚7
𝑛
−2
)
(2𝑎2 𝑏𝑐 3 )
(c) (−𝑎𝑏3 𝑐 2)2
−2𝑚0
∙(
𝑛−3
3
3
)
2
𝑢2
2
(f) ( 𝑣 ) + (−𝑢−2 𝑣)−2
11. Simply each expression.
(a) 3√2 − 4√2 + 7√2
(b) √27 + 2√75
(c) √3 × √5
(d) (2√6)(4√3)
(e) (3 + 2√5)(2 − √5)
(f) (4 − √2)(4 + √2)
12. Evaluate each expression by substituting the given value.
(a) 𝑥 2 − 2𝑥 + 3, if 𝑥 = −3
(b) −𝑥 2 + 5𝑥, if 𝑥 = −2
(c) 𝑥 3 + 2𝑥 2 + 3𝑥 − 6, if 𝑥 = −1
13. Expand the following expressions.
(a) 5(2x – 3y) – 6(x –2y)
(b) (x – 4)(x + 6)
(c) (x – 3)(7 – x)
(d) –2(3x + 1)(x + 3)
(e) (x + 1)(x + 2) – (2x + 1)(x – 4)
(f) (x + 5)2
14. Factor completely, if possible, the following expressions.
(a) 6x +3y – 27
(b) 15x3 – 35x2 – 5x
(c) x2 + 9
(d) x2 –7x + 12
(e) x2 +2x – 15
(f) x4 – 81
(g) 2x2 – x – 10
(h) 3x2 +10x – 8
(g) 4x2 – 8x + 3
(h) (x + 2)2 – 9
15. Solve each formula for the given variable.
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(a) 𝑠 = 2 𝑔𝑡 2 ; solve for 𝑔.
(b) 𝑃 = 2(𝑎 + 𝑏); solve for 𝑏.
(c) 𝑐 = 𝑎2 − 𝑏 2 ; solve for 𝑎.
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16. (a) List the first 10 prime numbers.
(b) List the first 10 perfect squares.
(c) List the prime factors of (i) 18, (ii) 48, and (iii) 165.
(d) List the first 5 multiples of (i) 3, and (ii) 8.
(e) List the greatest common factor (GCF) of (i) 12 & 54, and (ii) 24 & 108.
(f) List the least common multiple (LCM) of (i) 6 & 8 and (ii) 2, 3, &5.
17. Express each decimal as a percent.
(a) 0.56
(b) 0.00034
18. Express each percent as a fraction in lowest terms.
(a) 68%
(b) 22.5%
19. Express each percent as a decimal.
(a) 62%
(b) 524%
20. Graph the following sets.
(a) {𝑥| 𝑥 > 5, 𝑥 ∈ ℝ}
(b) {𝑥| 2 ≤ 𝑥 < 4, 𝑥 ∈ ℝ}
(c) {𝑥| 1 < 𝑥 < 5, 𝑥 ∈ ℤ}
21. Write in set notation.
(a)
(b)
(c)
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22. Solve for x. Graph the solution for the inequalities.
𝑥
(a)
7
1
− 7 = 10
(b)
2
3𝑥−2
5
=8
(d) 6𝑥 + 11 < 4𝑥 − 9
(c)2 𝑥 + 1 = 3 𝑥 − 2
(e) 1 − 2𝑥 ≥ 19
23. Does (3, 4) lie on the line with equation 3𝑥 − 2𝑦 = 1?
24. Write the equations of the line that
(a) has a slope of 2 and passes through (0, 4) in 𝑦 = 𝑚𝑥 + 𝑏 form.
(b) has m = 3 and passes through (3, 7) in 𝑦 = 𝑚𝑥 + 𝑏 form.
(c) passes through (2, 6) and (2, −8)
(d) passes through the points (3, 6) and (5, 7) in the form 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0, 𝑎, 𝑏, 𝑐 ∈ ℤ
(e) is perpendicular to the line 4x – 2y = 6 and the same y-intercept as the line 3x + 5y = 20 in the
form 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0, 𝑎, 𝑏, 𝑐 ∈ ℤ
25. Find the equation of the tangent line to the circle with center at (2, −2) and at the point (−1, 5).
26. Solve the following systems of linear equations.
(a)
4𝑥 + 2𝑦 = 30
−12𝑥 + 5𝑦 = −13
(b)
−14𝑥 + 20𝑦 = 4
7𝑥 − 10𝑦 = −9
(d)
7𝑥 + 6𝑦 = −8
8𝑥 − 9𝑦 = −25
(e)
0 = 9 + 45𝑥 − 9𝑦
−10 + 10𝑦 = 50𝑥
(c)
5
−2𝑥 + 5𝑦 = 27
7𝑥 + 7𝑦 = −21
27. Evaluate for each given function.
(a) 𝑓(𝑥) = 3𝑥 + 2, find 𝑓(10).
(b) 𝑔(𝑥) = 3𝑥 2 − 4𝑥, find g(2).
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(c) 𝑓(𝑥) = 𝑥 3 − 4 𝑥 2 , find 𝑓(− 3).
(d) ℎ(𝑥) = 3𝑥 + 3, find ℎ(2 − 𝑥).
(e) 𝑔(𝑥) = 𝑥 2 + 3, find 𝑔(𝑎2 ).
28. Find x.
(a)
(b)
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Part 2 – Calculator
29. Simplify the following. Give answers in scientific notation with the same number of significant
figures as in the least accurate factor.
(a)
(2.1423×104 )(4.23×10−3 )
(b)
7.123×106
(3.12×1014 )(6.82×10−23 )
(2.841×106 )(1.1×10−28 )
30. How many nanoseconds (1 nanosecond = 10–9 s) does it take a computer signal to travel 60 cm at a
rate of 2.4 × 10 10 cm/s?
31. The estimated masses of an electron and a proton are 9.11 × 10 −28 g and 1.67 × 10 −24 g,
respectively. Find the ratio of the mass of the proton to the mass of the electron.
32. Solve each proportion
(a)
x 4

3 9
𝑎
4
(b) 36 = 𝑎
(c)
11 2.8

2 .5
y
33. Solve the following questions. Round your answers to two (2) decimal places if necessary.
(a) What is 40% of 50?
(b) What number is 75% of 96?
(c) 12 is what percent of 60?
(d) 14 is 25% of what number?
(e) What is 110% of 110?
34. Express each fraction as a percent.
(a)
113
200
(b)
48
20
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35. Find x, correct to 3 significant figures.
(a)
(b)
x
36. Jason’s girlfriend lives in a house on Clifton
Highway which has equation 𝑦 = 8. The shortest
distance from Jason’s house to his girlfriend’s
house is 11.73 km. If Jason lives at (4, 1), what are
the coordinates of his girlfriend’s house?
37. A room is 7 m by 4 m and has a height of 3 m. Find the distance from a corner point on the floor to
the opposite corner of the ceiling.
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