Daily Practice · Higher Plus
January 2008 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2008, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2008 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2008
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2008On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd January 2008A rectangle is 21 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd January 2008Work out the nth term of the quadratic sequence 7, 17, 31, 49, ...
- 4th January 2008y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
- 5th January 2008In 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.
- 6th January 2008The probability of winning a game is 7/10. A player expects 35 wins. How many games did they play?
- 7th January 2008A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 8th January 2008Expand and simplify (9 + sqrt(7))(9 - sqrt(7)).
- 9th January 2008The point (-4, -3) lies on y = f(x). Write down its image on y = -f(x).
- 10th January 2008y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 4.
- 11th January 2008In a vector proof you find that vector PQ = 6a - 3b and vector RS = 12a - 6b. What does this show about PQ and RS?
- 12th January 2008A bag holds 8 red and n blue counters. The probability of taking a red is 8/15. Work out n.
- 13th January 2008On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th January 2008A block has mass 500 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.
- 15th January 2008Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 16th January 2008A train slows steadily from 14 m/s to rest in 10 seconds. Work out its deceleration.
- 17th January 2008A cuboid measures 9 cm by 13 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th January 2008A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th January 2008A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 20th January 2008x = 186 and y = 159, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st January 2008f(x) = 6x - 2 and g(x) = 6x + 2. Work out fg(5).
- 22nd January 2008y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 23rd January 2008A cuboid measures 10 cm by 13 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th January 2008A bag holds 4 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th January 2008On 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?
- 26th January 2008A car covers 880 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.
- 27th January 2008The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 28th January 2008y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 29th January 2008The 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.
- 30th January 2008A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 31st January 2008A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?