Daily Practice · Higher Plus
May 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2006 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2006Work out the nth term of the quadratic sequence 2, 1, 2, 5, ...
- 2nd May 2006A train slows steadily from 22 m/s to rest in 5 seconds. Work out its deceleration.
- 3rd May 2006A cuboid measures 7 cm by 12 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th May 2006A bag holds 7 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th May 2006A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 6th May 2006A car covers 170 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 7th May 2006The point (-6, 6) lies on y = f(x). Write down its image on y = f(x - 6).
- 8th May 2006y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 9th May 2006The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 10th May 2006A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 11th May 2006On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 12th May 2006Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
- 13th May 2006Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 14th May 2006y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 15th May 2006In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 16th May 2006The probability of winning a game is 7/8. A player expects 91 wins. How many games did they play?
- 17th May 2006A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 18th May 2006Simplify sqrt(48) + sqrt(12), giving your answer in the form a sqrt(b).
- 19th May 2006f(x) = 3x + 7 and g(x) = 2x - 8. Work out fg(4).
- 20th May 2006y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 16.
- 21st May 2006In a vector proof you find that vector PQ = a - 5b and vector RS = 5a - 25b. What does this show about PQ and RS?
- 22nd May 2006A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 23rd May 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?
- 24th May 2006A rectangle is 21 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th May 2006The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 26th May 2006A train slows steadily from 28 m/s to rest in 4 seconds. Work out its deceleration.
- 27th May 2006A cuboid measures 5 cm by 5 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th May 2006A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th May 2006A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 30th May 2006Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 31st May 2006A quadratic sequence starts 8, 19, 40, 71. Work out the second difference, and the coefficient of n^2.