Daily Practice · Higher Plus
January 2010 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2010, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2010 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2010
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2010A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 2nd January 2010On 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?
- 3rd January 2010x = 65 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th January 2010f(x) = 6x - 1 and g(x) = 2x + 3. Work out fg(3).
- 5th January 2010A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
- 6th January 2010A cuboid measures 14 cm by 15 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th January 2010A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th January 2010A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 9th January 2010A car covers 210 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th January 2010The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 11th January 2010y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 12th January 2010A cuboid measures 4 cm by 7 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th January 2010A bag holds 7 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th January 2010On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th January 2010Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
- 16th January 2010A quadratic sequence starts 13, 21, 31, 43. Work out the second difference, and the coefficient of n^2.
- 17th January 2010y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 18th January 2010The 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.
- 19th January 2010A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 20th January 2010A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 21st January 2010Simplify sqrt(72) + sqrt(72), giving your answer in the form a sqrt(b).
- 22nd January 2010Solve x^2 + 9x + 14 < 0.
- 23rd January 2010y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 9.
- 24th January 2010In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 25th January 2010The probability of winning a game is 7/8. A player expects 28 wins. How many games did they play?
- 26th January 2010On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 27th January 2010A rectangle is 14 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th January 2010Write x^2 + 2x + 2 in the form (x + a)^2 + b.
- 29th January 2010A train slows steadily from 14 m/s to rest in 5 seconds. Work out its deceleration.
- 30th January 2010In a vector proof you find that vector PQ = 6a - 3b and vector RS = 30a - 15b. What does this show about PQ and RS?
- 31st January 2010A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.