Daily Practice · Higher Plus
June 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2006 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2006y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 2nd June 2006A cuboid measures 4 cm by 12 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd June 2006A bag holds 3 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th June 2006On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th June 2006A block has mass 400 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th June 2006Solve x^2 - 2x - 8 > 0.
- 7th June 2006y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 8th June 2006The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 9th June 2006A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 10th June 2006A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 11th June 2006x = 70 and y = 43, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th June 2006Write x^2 - 6x + 11 in the form (x + a)^2 + b.
- 13th June 2006y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 81.
- 14th June 2006In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 15th June 2006The probability of winning a game is 1/4. A player expects 14 wins. How many games did they play?
- 16th June 2006On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 17th June 2006A car covers 540 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th June 2006Work out the coordinates of the turning point of y = x^2 - 6x + 12.
- 19th June 2006A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.
- 20th June 2006In a vector proof you find that vector PQ = a + 5b and vector RS = 3a + 15b. What does this show about PQ and RS?
- 21st June 2006A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 22nd June 2006A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 23rd June 2006Rationalise the denominator of 63/sqrt(7), giving your answer in its simplest form.
- 24th June 2006Simplify (x^2 - 9)/(x + 3).
- 25th June 2006y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 26th June 2006A cuboid measures 10 cm by 9 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th June 2006A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th June 2006On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 29th June 2006Simplify sqrt(80) + sqrt(180), giving your answer in the form a sqrt(b).
- 30th June 2006In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?