Mathematics Diagnostic Examination Guidance Examination Overview The Mathematics Examination will contain two sections. Section A contains fifteen 2-point questions and Section B contains five 4-point questions. No partial marks are given for any question, each question is either correct and receives full points, or incorrect and is given 0 points. The examination will cover three main topics; these topics and their approximate weighting on the examination are listed below: Algebra - 60% Geometry - 20% Statistics and Probability - 20% Algebra Solving one variable linear equations Converting between decimals and fractions Exponent Laws Negative exponents and the rational exponent law will not be on the examination Simplifying expressions Solving systems of equations Radicals Linear Functions Slope, y-intercept form Graphing linear functions and writing the equation of a linear function from a graph Determining the equation of a linear function from various pieces of information given Applications of linear functions (word problems) Factoring Greatest common factor ( ) Product / sum factoring x2 + bx + c Factoring trinomials where the leading coefficient is not 1 ( ax2 + bx + c, a 1) Difference of squares ( a2 b 2 ), Perfect square trinomials ( a 2 x 2 ± 2abx + b 2 ) PAGE 1 OF 13
Sample Questions for Algebra Section A 1. Determine the solution to the equation: 2( 3x 1) 1 = ( x 4). x = ( ) ( x + 1) 2. The expression 5 x 3 4 written in simplest form is: 3. When simplified fully, ( 3 6 )( 2 10 ) can be written as a mixed radical in the form a b. Determine the value of a + b. 4. The factored form of 3x 2 + 10x 8 is: 5. The expression ( a 2 b 3 ) 2 ( ab 4 ) written in simplest form is: 6. If 2a + 3b = 1 and 3a 2b = 8, find the values of a and b. a = b = 7. The cost, C, of renting a canoe is $35 plus an additional fee of $7.50 per hour, h. An expression to represent the canoe rental fee is: PAGE 2 OF 13
8. Write the equation of the linear function displayed on the graph below in the form y = mx + b : Section B 9. The intersection point of the two linear functions in the graph below is of the form a, b c. Determine the point of intersection. PAGE 3 OF 13
Geometry Parallel lines and transversal angle theorems Circle angle theorems Similar Triangles Translations and Reflections Two dimensional area problems (formulas are not provided) Squares, Rectangles Triangles Circles Special Triangles 30 60 90 and 45 45 90 Pythagoras Theorem Sample Questions 10. In ΔABC, see diagram below, the length of side AB is 7cm. Determine the perimeter of ΔABC, in the form a + b c, where a, b and c are all natural numbers. 11. In the circle below, the centre is denoted by O. Determine the value of p + q. PAGE 4 OF 13
12. Determine the area of the figure below, express your answer in the form a + bπ ( )cm 2, where a and b are natural numbers: 13. Triangle DEF is reflected across the line, l. The new coordinates of F after the reflection are: 14. In the diagram below AC is 20mm and AB is 25mm. The line MN is parallel to BC and AN is 16mm. Determine the length of AM: PAGE 5 OF 13
Statistics and Probability Measuring the centre of data - mean, median and mode Ways of reading data Bar graphs / Histograms Pie graphs Stem and leaf plots Probability With or without replacement Sample Questions 15. A student has four test scores of 72, 74, 74 and 80. After writing a fifth test, the average of his five scores is 76. What was the student s score on the fifth test? 16. A box contains 4 green marbles and 3 blue marbles. A marble is selected from the box, the colour is noted and then replaced. A second marble is then selected. Find the probability of drawing two green marbles. 17. A survey asked the ages of customers at a store. The data collected is displayed in the stem and leaf diagram below. Find the median age of the customers. 2 1 1 2 3 6 7 3 0 2 3 8 4 1 2 4 7 8 18. A box contains 5 red marbles and 3 blue marbles. A marble is selected from the box, the colour is noted and then a second marble is selected without replacement. Find the probability of drawing two blue marbles. PAGE 6 OF 13
Section A Section B 2 Section A 2 15 Section B 4 5 3 6 2 2 x 2 + bx + c ax 2 + bx + c a 2 b 2 PAGE 7 OF 13
Section A 1. 2( 3x 1) 1 = ( x 4) x = ( ) ( x + 1) 2. 5 x 3 4 3. ( 3 6 )( 2 10 ) a b a + b 4. 3x 2 + 10x 8 5. ( a 2 b 3 ) 2 ( ab 4 ) 6. 2a + 3b = 1, 3a 2b = 8 a b a = b = 7. 35 1 7.50 C C h PAGE 8 OF 13
8. y = ax + b Section B 9. a, b c PAGE 9 OF 13
30 60 90 45 45 90 10. ΔABC AB 7cm A = 60, B = 90 ΔABC a + b c a, b, c 11. O p + q PAGE 10 OF 13
12. a + bπ a, b 13. DEF l F 14. AC 20mm AB 25mm MN BC AN 16mm AM PAGE 11 OF 13
/ 15. 16. 17. 2 1 1 2 3 6 7 3 0 2 3 8 4 1 2 4 7 8 18. 5 3 1 1 2 PAGE 12 OF 13
Solutions to Sample Problems 1. x = 1 2. x 4 ( )( 2 10 ) = 12 15, 12 + 15 = 27 3. 3 6 4. 3x 2 + 10x 8 = ( 3x 2) ( x + 4) 5. ( a 2 b 3 ) 2 ( ab 4 ) = ( a 4 b 6 )( ab 4 ) = a 5 b 10 6. a = 2; b = 1 7. C = 7.5h + 35 or C = $7.50h + $35 8. y = 3 4 x 2 9. y = 1 x 1 2 y = 5 x 5 3, 5 2 6 10. ( 21+ 7 3)cm 11. p = 88; q = 44 p + q = 132 12. ( 16 + 2π )cm 2 13. ( 2,0) 14. AM = 20mm 15. 80 16. 16 49 17. 32 18. 3 2 = 3 8 7 28 PAGE 13 OF 13