Daily Practice · Higher Plus
June 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2009 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2009A block has mass 640 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd June 2009The point (0, 1) lies on y = f(x). Write down its image on y = -f(x).
- 3rd June 2009A train slows steadily from 40 m/s to rest in 4 seconds. Work out its deceleration.
- 4th June 2009In a vector proof you find that vector PQ = 6a + 3b and vector RS = 12a + 6b. What does this show about PQ and RS?
- 5th June 2009A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 6th June 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?
- 7th June 2009x = 35 and y = 23, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th June 2009Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 9th June 2009y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 10th June 2009A cuboid measures 6 cm by 9 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th June 2009A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th June 2009On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 13th June 2009A car covers 870 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.
- 14th June 2009f(x) = 3x - 5 and g(x) = 6x - 1. Work out fg(0).
- 15th June 2009y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 16th June 2009A cuboid measures 14 cm by 11 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th June 2009A bag holds 3 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th June 2009A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 19th June 2009Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 20th June 2009The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 21st June 2009y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 64.
- 22nd June 2009The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 23rd June 2009A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 24th June 2009On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th June 2009Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
- 26th June 2009A quadratic sequence starts 10, 24, 44, 70. Work out the second difference, and the coefficient of n^2.
- 27th June 2009A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.
- 28th June 2009In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 29th June 2009The probability of winning a game is 3/5. A player expects 21 wins. How many games did they play?
- 30th June 2009A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?