Daily Practice · Higher Plus
January 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2012 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2012y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 2nd January 2012A cuboid measures 6 cm by 11 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd January 2012A bag holds 6 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th January 2012On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th January 2012Simplify sqrt(72) + sqrt(98), giving your answer in the form a sqrt(b).
- 6th January 2012Solve x^2 - 9x + 14 > 0.
- 7th January 2012y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 8th January 2012The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 9th January 2012A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 10th January 2012A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 11th January 2012A rectangle is 29 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th January 2012Write x^2 - 6x - 12 in the form (x + a)^2 + b.
- 13th January 2012y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 9.
- 14th January 2012In 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.
- 15th January 2012The probability of winning a game is 5/8. A player expects 30 wins. How many games did they play?
- 16th January 2012On 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 January 2012Expand and simplify (6 + sqrt(6))(6 - sqrt(6)).
- 18th January 2012Work out the coordinates of the turning point of y = x^2 + 16x + 6.
- 19th January 2012A train slows steadily from 40 m/s to rest in 5 seconds. Work out its deceleration.
- 20th January 2012In a vector proof you find that vector PQ = 5a + 4b and vector RS = 10a + 8b. What does this show about PQ and RS?
- 21st January 2012A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 22nd January 2012A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 23rd January 2012A block has mass 850 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th January 2012Simplify (x^2 + 7x + 12)/(x + 3).
- 25th January 2012y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 26th January 2012A cuboid measures 4 cm by 6 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th January 2012A 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?
- 28th January 2012On 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?
- 29th January 2012x = 124 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th January 2012In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 31st January 2012y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.