Daily Practice · Higher Plus
January 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2009 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2009A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 2nd January 2009Rationalise the denominator of 55/sqrt(5), giving your answer in its simplest form.
- 3rd January 2009In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 4th January 2009y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 25.
- 5th January 2009In a vector proof you find that vector PQ = 5a - 3b and vector RS = 15a - 9b. What does this show about PQ and RS?
- 6th January 2009A bag holds 5 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 7th January 2009On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th January 2009Simplify sqrt(8) + sqrt(2), giving your answer in the form a sqrt(b).
- 9th January 2009Make x the subject of 5x + 5 = y(x + 5).
- 10th January 2009A train slows steadily from 17 m/s to rest in 4 seconds. Work out its deceleration.
- 11th January 2009A cuboid measures 15 cm by 3 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th January 2009A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th January 2009A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 14th January 2009A rectangle is 24 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th January 2009Write 2/(x - 6) + 7/(x + 3) as a single fraction.
- 16th January 2009y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 17th January 2009A cuboid measures 13 cm by 6 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th January 2009A bag holds 4 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th January 2009On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 20th January 2009Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 21st January 2009Solve 9x^2 + 15x + 4 = 0.
- 22nd January 2009y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 23rd January 2009The 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.
- 24th January 2009A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 25th January 2009A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 26th January 2009A block has mass 400 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th January 2009f(x) = 7x + 5. Work out the inverse function f^-1(x).
- 28th January 2009y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 16.
- 29th January 2009In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 30th January 2009The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 31st January 2009On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?