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Name _________________________________ Period_______ Date _______ Presumed Knowledge Below are topics listed in the IB syllabus as topics that are considered “Presumed Knowledge.” Students should be comfortable with most topics listed. If any of these topics do not seem familiar you should ask for clarification. PK1 Numbers and Algebra 1.01 Basic use of the four operations of arithmetic, using integers, decimals and simple fractions, including order of operations. Examples: 2(3 4 7) 62 ; 2 3 4 7 34 1.02 Prime numbers, factors and multiples. 1.03 Simple applications of ratio, percentage and proportion. 1.04 Absolute value a . Example: 4 7 3 1.05 Basic manipulation of simple algebraic expressions including factorization and expansion. Examples: ab ac a(b c); a 2 2ab b 2 a b ; a 2 b 2 (a b)(a b) 2 3x 2 5x 2 (3x 2)( x 1); xa 2a 2b ( x 2)(a b) 1.06 Solving linear equations in one variable. Example: 3( x 6) 4( x 1) 0 1.07 Solving a system of linear equations in two variables. Example: 3 x 4 y 13 2 x 2 y 1 1.08 Evaluating exponential expressions. Examples: a b , b Z; 24 1.09 Order relations <, ≤, >, ≥ and their properties. 1 16 Examples: (a b, c 0) ac bc;(a b, c 0 ac bc 1.10 1 2A Rearranging formulae. Example: A bh h 2 b 1.11 Evaluating formulae by substitution. Example: If x 3, then x 2 2 x 3 18 1.12 Intervals on the real number line. Example: 2 x 5, x R IB Math Studies Page 1 Scott PK2 Geometry and Trigonemetry 2.01 Basic geometric concepts: point, line, plane. 2.02 Simple two dimensional shapes and their properties, including perimeters and areas of circles, triangles, quadrilaterals and compound shapes. 2.03 The (x, y) coordinate plane. 2.04 Sine, cosine and tangent of acute angles. 2.05 Pythagorean Theorem. PK3 Probability and Statistics 3.01 The collection of data and its representation in bar charts, pie charts and pictograms. PK4 Financial Mathematics 4.01 Basic use of commonly accepted world currencies. Examples: Swiss franc (CHF); United States dollar (USD, $); British pound sterling (GBP, £); Japanese yen (JPY) On the pages that follow, you will find a set of questions addressing these topics. You may work in groups, but each student is to turn in a separate paper. Please circle all final answers. IB Math Studies Page 2 Scott Name _____________________________ Period_______ Date__________Score _________/40 Presumed Knowledge Directions: Use a pencil. You must show your work wherever possible. No work, no credit! Evaluate the expression: 4. 12 x 2 y 3 ( x y)3 when x = 2 and y = –3 1. 2 32 3 2. 7 x 2 when x = 2 and y = –3 y 5. What is 42% of 7500? 3. 2(3 4 7) = 6. If a $62 shirt is on sale at 20% off, what price do you pay? (Ignoring sales tax) 7. Put the values in increasing order. 0.0332 8. Put the values in increasing order. IB Math Studies –0.14 0.1569 6.3 –0.073 3 7 1 5 1 , , , , 5 13 3 4 6 Page 1 Scott Solve: 9. 2 5 x 3 x 1 10. You are making a model of the QE II. The ratio of the model to actual size is 1:500. The model is approximately 23.1 inches long. Estimate the actual length of the QE II. 11. Solve the following system of equations. 3x y 5 2 x 3 y 6 12. 6x 5 y 3 4 x 2 y 14 Tell whether each statement is true or false. If the statement is false, give a counterexample. 13. The absolute value of a positive number is always negative. 14. The absolute value of a negative number is always positive. 15. x x for every value of x. IB Math Studies Page 2 Scott Factor 16. x 2 3x 18 18. 9 x 2 30 x 25 17. 12 x 2 9 x 15 19. 16 x 2 9 Expand 20. 6 x(2 x 7) 21. x 6 22. (3 x 5)(2 x 7) 2 Solve 24. 3x 5 12x 23. 2(3 x) 22 2 x Solve and then sketch a graph of the inequality. 25. 3x 2 7 x 10 26. 15m 45 27. In which quadrant is the point (–3, 2)? IB Math Studies Page 3 Scott 9 28. Solve for C: F C 32 5 29. Solve for the missing side of the triangle. 30. Solve for the missing side of the triangle. 13.9 18 15 52o Find the Greatest common factor (GCF) and the least common multiple (LCM) of each pair of numbers 31. 10, 55 32. 35, 42 33. If there are 16 girls in a class of 28 students, what is the ratio of boys to girls, in simplest form? Fill in the appropriate inequality symbol to make each statement true. 34. a b, c 0 ac _____ bc 35. a b, c 0 ac _____ bc IB Math Studies Page 4 Scott 15 in 36. Determine the area of: 12 in 10 in 11 in 37. Determine the perimeter of: 7m 7m 10 m 4 ft 38. Determine the area of: 3 ft 2 ft 39. Determine the area of: d = 6 in 40. Determine the perimeter of the figure in question 39. IB Math Studies Page 5 Scott