Daily Practice · Higher Plus
January 2005 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2005, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2005y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 81.
- 2nd January 2005A cuboid measures 10 cm by 4 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd January 2005A bag holds 4 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th January 2005On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 5th January 2005A rectangle is 25 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th January 2005A quadratic sequence starts 7, 16, 31, 52. Work out the second difference, and the coefficient of n^2.
- 7th January 2005A train slows steadily from 16 m/s to rest in 4 seconds. Work out its deceleration.
- 8th January 2005A cuboid measures 11 cm by 13 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th January 2005A bag holds 7 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th January 2005A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 11th January 2005Expand and simplify (5 + sqrt(5))(5 - sqrt(5)).
- 12th January 2005Solve x^2 + 8x + 7 < 0.
- 13th January 2005y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 14th January 2005The 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.
- 15th January 2005A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 16th January 2005On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th January 2005A block has mass 710 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.
- 18th January 2005Write x^2 - 16x + 4 in the form (x + a)^2 + b.
- 19th January 2005y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
- 20th January 2005In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 21st January 2005The probability of winning a game is 1/2. A player expects 12 wins. How many games did they play?
- 22nd January 2005A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 23rd January 2005x = 65 and y = 25, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th January 2005Work out the coordinates of the turning point of y = x^2 - 12x - 15.
- 25th January 2005y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 9.
- 26th January 2005In a vector proof you find that vector PQ = 4a + 6b and vector RS = 20a + 30b. What does this show about PQ and RS?
- 27th January 2005A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 28th January 2005On 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?
- 29th January 2005A car covers 310 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 30th January 2005Simplify (x^2 + x - 20)/(x + 5).
- 31st January 2005A train slows steadily from 39 m/s to rest in 4 seconds. Work out its deceleration.