Daily Practice · Higher Plus
February 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2011 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2011A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd February 2011On 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?
- 3rd February 2011Simplify sqrt(8) + sqrt(18), giving your answer in the form a sqrt(b).
- 4th February 2011The point (2, 6) lies on y = f(x). Write down its image on y = f(-x).
- 5th February 2011y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 6th February 2011A cuboid measures 12 cm by 13 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th February 2011A bag holds 7 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th February 2011A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 9th February 2011A rectangle is 20 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th February 2011Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 11th February 2011y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 36.
- 12th February 2011The 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.
- 13th February 2011A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 14th February 2011On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 15th February 2011Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 16th February 2011f(x) = 2x - 3 and g(x) = 6x - 2. Work out fg(3).
- 17th February 2011A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.
- 18th February 2011In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 19th February 2011The probability of winning a game is 3/4. A player expects 60 wins. How many games did they play?
- 20th February 2011A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 21st February 2011A block has mass 780 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd February 2011The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 23rd February 2011y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 24th February 2011In a vector proof you find that vector PQ = 3a + 2b and vector RS = 6a + 4b. What does this show about PQ and RS?
- 25th February 2011A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 26th February 2011On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th February 2011x = 164 and y = 12, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th February 2011A quadratic sequence starts 6, 13, 22, 33. Work out the second difference, and the coefficient of n^2.