Grade 11 Tutorials - Maths Excellence

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Question 4 0 On the same system of axes, draw sketch graphs of = tan ( x + 45 ) y and y cos x x . Show clearly the co-ordinates of all intercepts with the axes, any points of intersection of the two graphs and draw any asymptotes, indicating the equation/s where applicable. Question 5 Sketched below is a section of the graphs of f ( x) = a cosbx and g( x) csin dx = for ∈( −135 ) 0 ; 45 0 = . ^y A (0° ; 1) O B E >x C D (90 °; −2 ) 5.1 Calculate the values of a , b, c and d . 5.2 What is the period of f ( x) = a cosbx 5.3 What is the range of g( x) = csin dx 5.4 Calculate the co-ordinates of B, C and E. These points are either intercepts with the x axis turning points. 0 0 5.5 Determine the value of f ( 45 ) − g( 45 ) Grade 11 - 8 - Tutorials
Grade 11 Tutorial Algebra and Equations 1. Solve for x : (Leave irrational answers in simplest surd form) x 1.2 ( x − 7 )( x − 5) = 3 1.1 3 2 −17x + 15 = 0 1.3 1 x = 1+ 1.4 x 3 − 2x 2 − x − 2 0 x = 1.5 2 1 ≤ x + 1 x −1 1.6 2x 2 + x > 6 1.7 x 1 3 3 x 1 − ≤ 1.8 ( − 3 ) 2 < 40 − x x 1.9 2 = 20 (correct to 3 decimal places) 1.10 x 4 = 2 2 2. Solve for x and y : 2 2 2.1 2 x − y = 5 and x − xy + y + 4 = 0 2.2 xy +12 = 0 and 2 y = x + 10 2 2 2.3 2 x + 3y = 4 and x − xy − y = −1 3. For which values of k does the straight line y = 2x + k touch the hyperbola xy = −18 at a single point? 4. The product of two positive integers is 160. The difference between them is 27. What are the numbers? 5. The members of a school photographic club decided to all pay the same amount to buy new equipment for R1 000. One of the members negotiated a 27,5% discount on the equipment and the amount that each had to pay was calculated. Then 4 more people joined the club. This meant that each member had to pay R4 less than was originally announced. How many members were originally in the club? 6. A trip to a meeting 60 km from home took 5 minutes less than the return trip as the peak hour traffic reduced the average speed for the return trip by 10 km/h. Calculate the average speed travelled on the trip to the meeting. Grade 11 - 9 - Tutorials
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Grade 11 Tutorials - Maths Excellence

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