Daily Practice · Higher Plus
March 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 2009 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 2009The probability of winning a game is 3/4. A player expects 18 wins. How many games did they play?
- 2nd March 2009A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 3rd March 2009Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 4th March 2009f(x) = 3x - 6 and g(x) = 6x + 7. Work out fg(3).
- 5th March 2009y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 6th March 2009In a vector proof you find that vector PQ = 2a + b and vector RS = 8a + 4b. What does this show about PQ and RS?
- 7th March 2009A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 8th March 2009On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th March 2009A block has mass 870 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th March 2009The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 11th March 2009y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 12th March 2009A cuboid measures 10 cm by 14 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th March 2009A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th March 2009A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 15th March 2009x = 76 and y = 35, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th March 2009A quadratic sequence starts 5, 17, 37, 65. Work out the second difference, and the coefficient of n^2.
- 17th March 2009y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 36.
- 18th March 2009A cuboid measures 10 cm by 13 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th March 2009A bag holds 4 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th March 2009On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st March 2009A car covers 830 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd March 2009Solve x^2 - 9x + 8 < 0.
- 23rd March 2009A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
- 24th March 2009The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 25th March 2009A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 26th March 2009A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 27th March 2009Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 28th March 2009Write x^2 + 16x - 14 in the form (x + a)^2 + b.
- 29th March 2009y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 30th March 2009In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 31st March 2009The probability of winning a game is 7/10. A player expects 91 wins. How many games did they play?